Invariant geometric motions of space curves

Abstract

Motions of space curves in similarity and centro-affine geometries are studied. It is shown that the geometric motions of inextensible space curves in similarity and centro-affine geometries are closely related to integrable equations. Several gauge equivalent integrable equations are derived through the relationship between the curvature and graph of the curves. Motion of space curves corresponding to travelling wave solutions to the KdV flow in centro-affine geometry is discussed in detail. © Springer-Verlag Berlin Heidelberg 2005.